Review Conceptual Example 7 as background for this problem. Two charges are fixed in place with a separation d. One charge is positive and has twice (n = 2) the magnitude of the other charge, which is negative. The positive charge lies to the left of the negative charge, as in the figure. Relative to the negative charge, locate the two spots on the line through the charges where the total potential is zero.

Positive distance to the left from -q:

k•2•q/(d-x) = k•q/x
2x=d-x
x=d/3
Positive distance to the right of -q
k•2•q/(d+x) = k•q/x
2x=d+x
x=d

To solve this problem, we need to find two spots on the line between the charges where the total electric potential is zero, relative to the negative charge. Let's break this down step by step:

Step 1: Understand the scenario
In this problem, we have two charges fixed in place with a separation d. One charge is positive and has twice the magnitude of the other charge, which is negative. The positive charge is located to the left of the negative charge.

Step 2: Understand electric potential
Electric potential is the amount of electric potential energy per unit charge at a specific point in an electric field. The total electric potential at a particular point is the sum of the electric potentials created by individual charges.

Step 3: Apply the concept
To find the spots on the line where the total electric potential is zero relative to the negative charge, we need to consider the electric potentials created by the two charges.

Let's denote the magnitudes of the positive and negative charges as Q and q respectively. We are given that Q = 2q.

Step 4: Analyze the charges
Considering a test charge experiencing the electric potential due to the positive charge, we know that the electric potential (V) is given by V = kQ/r, where k is the electrostatic constant, Q is the charge magnitude, and r is the distance from the charge.

Similarly, the electric potential due to the negative charge is V = -kq/r.

Since we want to find the points on the line where the total potential is zero, we can set up the equation: V_positive + V_negative = 0.

Step 5: Solve the equation
Substituting the expressions for V_positive and V_negative, we have k(2q)/r + (-kq)/r = 0.

Simplifying the equation, we get 2q - q = 0.

Thus, q = 0.

Since q represents the magnitude of a charge, we cannot have a charge with zero magnitude. Hence, there is no point on the line where the total potential is zero relative to the negative charge.

Step 6: Conclusion
After analyzing the problem and solving the equation, we find that there is no point on the line between the charges where the total electric potential is zero, relative to the negative charge.

Remember, understanding the concept and applying it to specific scenarios will help you solve problems like these. Keep practicing and reviewing different examples to strengthen your understanding.

To find the two spots on the line through the charges where the total potential is zero, we can use the concept of electric potential.

Let's denote the positive charge as q1 and the negative charge as q2.
Given that q1 is positive and has twice the magnitude of q2, we can write q1 = 2q2.

The electric potential due to a point charge q at a distance r from it is given by V = k*q/r, where k is the electrostatic constant.

To find the potential at a point on the line through the charges, we need to consider the potential due to both charges.

Let's consider a point P on the line, at a distance x from q2. The distance between the two charges is d.

The potential due to q1 at point P is V1 = k*q1/(d - x).
The potential due to q2 at point P is V2 = k*q2/x.

Since the total potential at point P is zero, we have V1 + V2 = 0.

Substituting the values of q1 and q2, we get:
(k*2q2)/(d - x) + (k*q2)/x = 0.

Multiplying through by x(d - x), we get:
2q2*x + q2*(d - x) = 0.

Simplifying the equation, we have:
2q2x + q2d - q2x = 0.

Combining like terms, we have:
q2x + q2d = 0.

Dividing through by q2, we get:
x + d = 0.

Therefore, the two spots on the line through the charges where the total potential is zero are located at x = -d and x = 0.